I read this book in the early 1970s when I was a chem major and a physicist wannabe. It was a perfect introduction to the QM formalism. Keep in mind, the title says "primer". It is, but after reading this book, you'll be ready for Albert Messiah's magnificent "non-primer". Gillespie's book is one of those little gems that are short and where every page is worth reading. It is accessible, satisfying, a great first-step.
So, why did I come back here after all these years? My CS colleagues are all a buzz about quantum computing, but they don't know the basics. No way am I going to lend them MY copy of this book but I thought I'd buy another one and pass it around.